I know that you thought you were providing a counterexample (which is odd, since I wasn't making some kind of universal claim) but yeah, they are. Branching into groceries represented a pretty bold diversification. I'm pretty sure they've talked about even providing banking services. They're about as diversified as a dedicated brick and mortar retailer can possibly be, and it's not hard to see why: they control their existing niches and they want to continue growing.
I wasn't aiming for a counterexample so much as an illustration of the fact that whether a company is diversified or not is a matter of definition.
Is a company diversified if it operates in related markets in the same sector, like a bank that does retail and business banking? Is a company diversified if operations outside their core business are only a small fraction of their turnover, like an oil company that has a small renewables operation?
If the purpose of diversification is to keep the company afloat if there's a downturn in one market, these properties are important. Being in retail and business banking won't help if the entire banking sector has problems, and 1% of your business won't keep you afloat if the other 99% of your business is sinking.
How many companies the size of Google are NOT heavily diversified? Think GE, 3M, etc.